Sunday, May 29, 2011

Tornados and global warming - how do we judge predictions?

We can't forecast a tornado, and we can't predict how a tornado will behave. We can, however, characterize tornadogenic climates and geographies. As CO2 accumulates and the earth warms virtually all terrestrial climates will change. Because climates will change they will all become more or less tornadogenic. This seems self-evident; I don't think there's any controversy here.

There is lots of controversy, however, when we try to understand the causes of the great American Tornados of 2011. There is controversy too, when we try to predict what will happen over the decades to come. Will, for example, geographic regions experience an increase in tornados as the earth warms, only to see a decrease when it warms still more? Will "Tornado zones" migrate north, so that Arkansas will have fewer, but Minnesota more?

Insurance companies would dearly love to know. So would homeowners contemplating installation of a basement emergency shelter. Given the purported limitations of historic data, how can insurance companies and homeowners make decisions?

Consider the case of a fair coin. Flip the coin ten times and you get this: TTTTTTTTTT - ten Tails. What's the chance of a Head on the next toss?

It's a trick question. I said it was a fair coin. The chance of Heads is 1/2, just as it was for the previous 10 tosses. Reverend Bayes does not apply.

Now consider that the coin has been altered; it's no longer a fair coin. Flip the coin ten times and you get this: TTTTTTTTH. What's our best estimate of the chance of a Head on the next toss?

It's 1/10.We don't know anything about the coin, so our best estimate of future performance is past performance.

So we can measure tornados like biased coin tosses and, in 30 years or so, we'll get some reasonable answers.

... The process of iterating on internally consistent models that make testable predictions, and revising those models when predictions fail, has transformed human history. It is the only guide we have to developing better medicines, understanding the universe, or predicting the consequences of CO2 accumulation...

Consider our biased coin. We might speculate that a variable gravitational field is causing bias. We may predict that if gravity is varying, then local clocks should diverge from distant clocks. Clocks seem unrelated to coin toss, but if we do find clock drift, then our varying gravity explanation for both coin bias and clock drift is strengthened. We can use that new understanding to make more accurate predictions of future coin toss outcomes.

In a connected system, like a climate, a model can be validated by shorter series of multiple measures. So a model that predicted tornadogenic weather might take decades to validate, but a model that predicts summer storms, winter snow and average temperatures might be validated in a shorter time.

At least that's what insurance companies must be banking on. There's a vast amount of money at stake, a good model would be worth a lot. Particularly if it were private ...